Question

In $\Delta PQR$, right-angled at $Q,PR+QR=25cm$ and $PQ=5cm$. Determine the values of $\sin P,\cos P$ and $\tan P$.

Answer 1

Let $PR=x$

$QR=25-x$

${\left(PQ\right)}^2+(QR{)}^2=(PR{)}^2$

$5^2+{(25-x)}^2=x^2$

$25+(25{)}^2-50x+x^2=x^2$

$\Rightarrow 50x=(25{)}^2+25$

$\Rightarrow 50x=650$

$\Rightarrow x=13$

$\therefore PR=13QR=25-13=12$

$\cos P=\frac{PQ}{PR}=\frac{5}{13}$

$\sin P=\frac{QR}{PR}=\frac{12}{13}$

$\tan P=\frac{QR}{PR}=\frac{12}{5}$